Cluster variation study of the underpotential deposition of Cu on Au(111) in the presence of bisulfate

A cluster variation method is developed to study the phase transitions and the structures of phases which occur at the fluid-crystal interface during the underpotential deposition of a metal on an electrode in the presence of an anion, such as bisulfate. In addition to the possibility of first-order condensation phase transitions occurring during the deposition of a metal, the steric repulsion of adsorbed anions can also cause an order-disorder transition. Using clusters containing six adsorption sites, the method is applied to the underpotential deposition of copper on (111) gold in the presence of bisulfate. In order to fix a constant in the expression for the entropy, the effect of the hard-core exclusion of a pair of first-neighbor bisulfates, in addition to the effect of finite interactions, is calculated exactly in the limit of high temperature. The cluster method yields two coupled adsorption isotherms for copper and bisulfate in terms of their activities and coverages. The resulting isotherms show an order-disorder transition due to the hard-core exclusion of neighboring bisulfate ions, as well as two first-order phase transitions in the copper and bisulfate coverages which correspond to the two spikes in the experimental voltammogram. The cluster method also gives the local structure of the phases which occur as the voltage is changed. (C) 1998 American Institute of Physics.